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International Journal of Modern Physics B

Tuning from fermi liquid to SYK-like non-fermi liquid via scattering momentum cutoff in a bound state system

Chen-Huan Wu

Published Jan 8, 2026• 0 citations
Publisher

Abstract

While bound states are typically treated as long-lived quasiparticles with slow momentum and current relaxation in a Fermi liquid (FL) phase, this paper investigates their properties within a non-Fermi liquid (NFL) phase exhibiting Sachdev–Ye–Kitaev (SYK)-like ensemble behavior. We establish a fundamental relation between the UV cutoff of the relative scattering momentum, [Formula: see text], and the emergence of this SYK-like physics, a connection which has not been previously explored. We find that [Formula: see text] directly controls the statistical properties of the coupling term. In the limit [Formula: see text], the large number of momentum steps causes the coupling to behave as a Gaussian or Chi-square random variable, fulfilling the conditions for SYK-like chaos. This reveals [Formula: see text] as a tuning parameter for a phase transition: the [Formula: see text] limit corresponds to the NFL phase with ill-defined bound states, while a finite [Formula: see text] corresponds to a (disordered) FL phase with well-defined bound state quasiparticles. Furthermore, we show that pair condensation, which emerges at a critical temperature, competes with and suppresses the NFL phase. Finally, we note that in the case of large-range condensation, a homogeneous character emerges and thermalization is observed, where high-energy eigenstates show low overlap with low-entanglement states.

DOI
10.1142/s0217979226500396

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The bound state is treated as a long-lived quasiparticle with slow momenta and current relaxation in fermi liquid phase. In this paper, we discuss the realization of ensemble behavior in a 3D fermi gas system in non-fermi liquid phase. We reveal the relation between UV cutoff of relative momentum ΛqΛ_{q}Λq​ and its ensemble behavior. The behavior of a bound state system has rarely been investigated before, and the relation between the scattering momentum and the physics has not yet been explored before (to best of our knowledge). We found that the cutoff ΛqΛ_{q}Λq​ directly related to the distribution and statistical variance of coupling term, which becomes Gaussian variable (or Chi-square variable) in limit (i.e., with a large step number of a fractional distance Λq−1→∞Λ_{q}^{-1}\rightarrow\inftyΛq−1​→∞). Also, we show that the different Λq−1Λ_{q}^{-1}Λq−1​ lending support to different phases, including non-fermi liquid phase and (disordered) fermi liquid phase, which correspond to ill-defined and well-defined bound states, respectively. The pair condensation induced by local coupling, which happen at critical temperature, would suppresses the non-fermi liquid for constant on-site coupling (it is not the case when the coupling be variant). % We deduce the free energy density and the divergent behaviors of anomalous propagator in this case. % Finally, we also present a discussion of ensembles of level statistic that depending on which symmetry class the system belongs to, and that can be controlled by the type of disorder. Further, when the range of condensation is larger, the homogeneous character will emerge and the thermalization can be observed where eigenstates with higher energy has lower overlap with the low-entangled states.
Periodically driven quantum matter can realize exotic dynamical phases. In order to understand how ubiquitous and robust these phases are, it is pertinent to investigate the heating dynamics of generic interacting quantum systems. Here we study the thermalization in a periodically driven generalized Sachdev-Ye-Kitaev (SYK) model, which realizes a crossover from a heavy Fermi liquid (FL) to a non-Fermi liquid (NFL) at a tunable energy scale. Developing an exact field theoretic approach, we determine two distinct regimes in the heating dynamics. While the NFL heats exponentially and thermalizes rapidly, we report that the presence of quasiparticles in the heavy FL obstructs heating and thermalization over comparatively long timescales. Prethermal high-frequency dynamics and possible experimental realizations of nonequilibrium SYK physics are discussed as well.
Non-Fermi liquids (NFLs) are a class of strongly interacting gapless fermionic systems without long-lived quasiparticle excitations.An important group of NFL models feature itinerant fermions coupled to soft bosonic fluctuations near a quantum-critical point and are widely believed to capture the essential physics of many unconventional superconductors.However, numerically, the direct observation of a canonical NFL behavior in such systems, characterized by a power-law form in the Green's function, has been elusive.Here, we consider a Sachdev-Ye-Kitaev (SYK)-like model with random Yukawa interaction between critical bosons and fermions (dubbed the Yukawa-SYK model).We show that it is immune from the minus-sign problem and hence can be solved exactly via large-scale quantum Monte Carlo simulation beyond the large-N limit accessible to analytical approaches.Our simulation demonstrates that the Yukawa-SYK model features "self-tuned quantum criticality"; namely, the system is critical independent of the bosonic bare mass.We put these results to the test at finite N, and our unbiased numerics reveal clear evidence of these exotic quantum-critical NFL properties-the power-law behavior in the Green's function of fermions and bosons-which propels the theoretical understanding of critical Planckian metals and unconventional superconductors.
We study the thermalization, after sudden and slow quenches, in an interacting model having a quantum phase transition from a Sachdev-Ye-Kitaev (SYK) non-Fermi liquid (NFL) to a Fermi liquid (FL). The model has SYK fermions coupled to noninteracting lead fermions and can be realized in a graphene flake connected to external leads. A sudden quench to the NFL leads to rapid thermalization via collapse-revival oscillations of the quasiparticle residue of the lead fermions. In contrast, the quench to the FL shows multiple prethermal regimes and much slower thermalization. In the slow quench performed over a time τ, we find that the excitation energy generated has a remarkable intermediate-τ nonanalytic power-law dependence, τ−η with η<1, which seemingly masks the dynamical manifestation of the initial residual entropy of the SYK fermions. Our study gives an explicit demonstration of the intriguing contrasts between the out-of-equilibrium dynamics of a NFL and a FL in terms of their thermalization and approach to adiabaticity.
Several condensed-matter platforms have been proposed recently to realize the Sachdev-Ye-Kitaev (SYK) model in their low-energy limit. In these proposed realizations, the characteristic SYK behavior is expected to occur under certain assumptions about the underlying physical system that (i) render all bilinear terms small compared to four-fermion interactions and (ii) ensure that the coupling constants are approximately all-to-all and independent random variables. In this work we explore, both analytically and numerically, the family of models that arises when we relax these assumptions in ways motivated by real physical systems. By relaxing (i) and allowing large bilinear terms, we obtain a novel, exactly solvable cousin of the SYK\mathrm{SYK}SYK model. It exhibits two distinct phases separated by a quantum phase transition characterized by a power-law, ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}1/3}$, scaling of the low-energy spectral density, despite being a noninteracting model. By relaxing (ii), we obtain close relatives of the SYK\mathrm{SYK}SYK model which exhibit interesting behaviors, including a chaotic non-Fermi liquid phase with continuously varying fermion scaling dimension, and a phase transition to a disordered Fermi liquid as a function of interaction range and disorder length scale.
The Sachdev-Ye-Kitaev (SYK) model describes interacting fermionic zero modes in zero spatial dimensions, e.g. quantum dot, with interactions strong enough to completely washout quasiparticle excitations in the infrared. In this note, we consider the complex-valued SYK model at temperature TTT coupled to a zero temperature reservoir by a quench. We find out that the tunneling current dynamics reveals a way to distinguish the SYK non-Fermi liquid (nFL) initial state of the subsystem from the disordered Fermi liquid. Temperature dependent contribution to the current's half-life scales linearly in TTT at low temperatures for the SYK nFl state, while for the Fermi liquid it scales as T2T^2T2. This provides a characteristic signature of the SYK non-Fermi liquid in a non-equilibrium measurement.